Quick Answer
Delta measures how much an option's premium changes for a one-unit change in the underlying futures price. Call delta is positive, running about 0 to +1; put delta is negative, running about 0 to minus 1. Delta also approximates the hedge ratio, the number of futures contracts a position behaves like.
Intrinsic and time value describe what a premium is made of. Delta describes how that premium moves. It is the option's sensitivity to the underlying futures price.
What Delta Measures
Delta measures how much an option's premium changes for a one-unit change in the underlying futures price. A call is the right to go long futures at the strike, and a put is the right to go short, so the two react to the underlying in opposite directions.
- A call's premium rises when the underlying futures price rises.
- A put's premium falls when the underlying futures price rises, and rises when the underlying falls.
Sign and Range
The direction of the reaction is baked into delta's sign, and this is where most delta questions are won or lost.
- Call delta is positive, ranging from about 0 to +1.
- Put delta is negative, ranging from about 0 to minus 1.
- In absolute value, both run 0 to 1.
Memory Aid: Calls carry a plus because they climb with the underlying; puts carry a minus because they move against it. Same size, opposite sign.
Exam Tip: Gotchas
- Put delta is negative. A put loses premium as the underlying futures price rises. A frequent trap treats every delta as positive, but only calls have positive delta, while puts run 0 to minus 1.
Delta by Moneyness
How strongly an option tracks the underlying depends on how deep in-the-money (ITM), at-the-money (ATM), or out-of-the-money (OTM) it is.
| Moneyness | Call delta | Put delta (absolute value) |
|---|---|---|
| Deep in-the-money | approaches +1 | approaches 1 |
| At-the-money | roughly +0.5 | roughly 0.5 |
| Deep out-of-the-money | approaches 0 | approaches 0 |
- Deep in-the-money options move nearly one-for-one with the underlying futures, with delta near 1 in absolute value.
- At-the-money options have a delta of roughly 0.5.
- Out-of-the-money options have a delta approaching 0 and barely respond to underlying moves.
Delta as the Hedge Ratio
Beyond sensitivity, delta doubles as a practical hedging tool.
- Delta approximates the hedge ratio: how many futures contracts an option position behaves like, and therefore how many are needed to offset its directional risk.
- An underlying futures contract has a delta of 1. An option with a delta of 0.5 behaves like half a futures contract, so it takes roughly two such options to equal one futures contract.
- Because delta shifts as the underlying moves, the hedge ratio is dynamic, not fixed.
Think of it this way: delta is the exchange rate between an option and the futures it tracks. A delta of 0.5 means each option is worth half a futures contract in price movement, so you line up two options against one future to stay balanced. As the market moves and delta drifts, that exchange rate resets, which is why a hedge has to be adjusted rather than set once.
Exam Tip: Gotchas
- The hedge ratio is dynamic, not a fixed number. Delta changes as the underlying moves and as expiration nears, so the number of contracts needed to stay hedged keeps shifting. An answer that treats the hedge ratio as locked in for the life of the trade is wrong.